Properties

Label 224.3.w.a.43.8
Level 224
Weight 3
Character 224.43
Analytic conductor 6.104
Analytic rank 0
Dimension 192
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 224.w (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.10355792167\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(48\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 43.8
Character \(\chi\) \(=\) 224.43
Dual form 224.3.w.a.99.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.75066 - 0.967050i) q^{2} +(-1.86844 - 4.51082i) q^{3} +(2.12963 + 3.38595i) q^{4} +(0.599529 - 1.44739i) q^{5} +(-1.09118 + 9.70379i) q^{6} +(-1.87083 + 1.87083i) q^{7} +(-0.453865 - 7.98712i) q^{8} +(-10.4924 + 10.4924i) q^{9} +O(q^{10})\) \(q+(-1.75066 - 0.967050i) q^{2} +(-1.86844 - 4.51082i) q^{3} +(2.12963 + 3.38595i) q^{4} +(0.599529 - 1.44739i) q^{5} +(-1.09118 + 9.70379i) q^{6} +(-1.87083 + 1.87083i) q^{7} +(-0.453865 - 7.98712i) q^{8} +(-10.4924 + 10.4924i) q^{9} +(-2.44927 + 1.95412i) q^{10} +(-8.17903 + 19.7459i) q^{11} +(11.2943 - 15.9328i) q^{12} +(1.00363 + 2.42299i) q^{13} +(5.08437 - 1.46600i) q^{14} -7.64910 q^{15} +(-6.92938 + 14.4216i) q^{16} -22.9978i q^{17} +(28.5154 - 8.22199i) q^{18} +(-28.2373 + 11.6963i) q^{19} +(6.17757 - 1.05242i) q^{20} +(11.9345 + 4.94343i) q^{21} +(33.4140 - 26.6589i) q^{22} +(19.0036 + 19.0036i) q^{23} +(-35.1804 + 16.9708i) q^{24} +(15.9422 + 15.9422i) q^{25} +(0.586128 - 5.21240i) q^{26} +(26.3367 + 10.9090i) q^{27} +(-10.3187 - 2.35037i) q^{28} +(23.1121 - 9.57336i) q^{29} +(13.3910 + 7.39707i) q^{30} -12.8494i q^{31} +(26.0774 - 18.5463i) q^{32} +104.352 q^{33} +(-22.2400 + 40.2613i) q^{34} +(1.58620 + 3.82944i) q^{35} +(-57.8720 - 13.1820i) q^{36} +(-17.0724 + 41.2165i) q^{37} +(60.7448 + 6.83069i) q^{38} +(9.05443 - 9.05443i) q^{39} +(-11.8326 - 4.13159i) q^{40} +(16.4556 - 16.4556i) q^{41} +(-16.1127 - 20.1955i) q^{42} +(-9.75224 + 23.5440i) q^{43} +(-84.2770 + 14.3576i) q^{44} +(8.89615 + 21.4772i) q^{45} +(-14.8914 - 51.6463i) q^{46} -40.5701 q^{47} +(78.0006 + 4.31118i) q^{48} -7.00000i q^{49} +(-12.4924 - 43.3262i) q^{50} +(-103.739 + 42.9700i) q^{51} +(-6.06676 + 8.55832i) q^{52} +(-79.5206 - 32.9385i) q^{53} +(-35.5571 - 44.5669i) q^{54} +(23.6765 + 23.6765i) q^{55} +(15.7916 + 14.0934i) q^{56} +(105.519 + 105.519i) q^{57} +(-49.7195 - 5.59090i) q^{58} +(61.8251 + 25.6088i) q^{59} +(-16.2897 - 25.8995i) q^{60} +(-85.2735 + 35.3215i) q^{61} +(-12.4260 + 22.4950i) q^{62} -39.2592i q^{63} +(-63.5880 + 7.25014i) q^{64} +4.10872 q^{65} +(-182.685 - 100.914i) q^{66} +(-7.35639 - 17.7599i) q^{67} +(77.8695 - 48.9767i) q^{68} +(50.2147 - 121.229i) q^{69} +(0.926352 - 8.23798i) q^{70} +(-1.36506 + 1.36506i) q^{71} +(88.5666 + 79.0422i) q^{72} +(-30.6133 + 30.6133i) q^{73} +(69.7465 - 55.6462i) q^{74} +(42.1252 - 101.699i) q^{75} +(-99.7379 - 70.7015i) q^{76} +(-21.6397 - 52.2428i) q^{77} +(-24.6073 + 7.09515i) q^{78} -51.5418 q^{79} +(16.7194 + 18.6757i) q^{80} -5.63591i q^{81} +(-44.7217 + 12.8948i) q^{82} +(-16.5575 + 6.85835i) q^{83} +(8.67780 + 50.9374i) q^{84} +(-33.2868 - 13.7878i) q^{85} +(39.8411 - 31.7866i) q^{86} +(-86.3674 - 86.3674i) q^{87} +(161.425 + 56.3648i) q^{88} +(35.4834 + 35.4834i) q^{89} +(5.19540 - 46.2023i) q^{90} +(-6.41063 - 2.65537i) q^{91} +(-23.8748 + 104.816i) q^{92} +(-57.9614 + 24.0084i) q^{93} +(71.0245 + 39.2334i) q^{94} +47.8826i q^{95} +(-132.383 - 82.9779i) q^{96} +92.1133 q^{97} +(-6.76935 + 12.2546i) q^{98} +(-121.365 - 293.001i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192q + O(q^{10}) \) \( 192q + 80q^{10} + 96q^{12} - 20q^{16} - 60q^{18} - 260q^{22} + 64q^{23} - 144q^{24} - 200q^{26} + 192q^{27} - 40q^{30} + 40q^{32} + 120q^{34} + 464q^{36} + 504q^{38} - 384q^{39} + 360q^{40} - 96q^{43} + 52q^{44} + 64q^{46} - 104q^{48} - 312q^{50} - 384q^{51} - 320q^{52} + 160q^{53} - 576q^{54} - 512q^{55} - 196q^{56} - 360q^{58} - 872q^{60} + 128q^{61} - 408q^{62} + 832q^{66} + 160q^{67} + 856q^{68} - 384q^{69} + 336q^{70} + 1488q^{72} + 308q^{74} + 768q^{75} + 1024q^{76} - 224q^{77} - 408q^{78} + 1024q^{79} - 1040q^{80} - 240q^{82} - 1384q^{86} + 896q^{87} - 560q^{88} - 1320q^{90} - 380q^{92} - 936q^{94} - 1088q^{96} - 512q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.75066 0.967050i −0.875330 0.483525i
\(3\) −1.86844 4.51082i −0.622814 1.50361i −0.848385 0.529380i \(-0.822425\pi\)
0.225571 0.974227i \(-0.427575\pi\)
\(4\) 2.12963 + 3.38595i 0.532407 + 0.846489i
\(5\) 0.599529 1.44739i 0.119906 0.289478i −0.852518 0.522697i \(-0.824926\pi\)
0.972424 + 0.233219i \(0.0749259\pi\)
\(6\) −1.09118 + 9.70379i −0.181863 + 1.61730i
\(7\) −1.87083 + 1.87083i −0.267261 + 0.267261i
\(8\) −0.453865 7.98712i −0.0567331 0.998389i
\(9\) −10.4924 + 10.4924i −1.16583 + 1.16583i
\(10\) −2.44927 + 1.95412i −0.244927 + 0.195412i
\(11\) −8.17903 + 19.7459i −0.743548 + 1.79508i −0.152748 + 0.988265i \(0.548812\pi\)
−0.590800 + 0.806818i \(0.701188\pi\)
\(12\) 11.2943 15.9328i 0.941195 1.32774i
\(13\) 1.00363 + 2.42299i 0.0772027 + 0.186384i 0.957769 0.287540i \(-0.0928373\pi\)
−0.880566 + 0.473923i \(0.842837\pi\)
\(14\) 5.08437 1.46600i 0.363169 0.104714i
\(15\) −7.64910 −0.509940
\(16\) −6.92938 + 14.4216i −0.433086 + 0.901352i
\(17\) 22.9978i 1.35281i −0.736529 0.676406i \(-0.763537\pi\)
0.736529 0.676406i \(-0.236463\pi\)
\(18\) 28.5154 8.22199i 1.58419 0.456777i
\(19\) −28.2373 + 11.6963i −1.48617 + 0.615593i −0.970480 0.241180i \(-0.922465\pi\)
−0.515693 + 0.856774i \(0.672465\pi\)
\(20\) 6.17757 1.05242i 0.308879 0.0526212i
\(21\) 11.9345 + 4.94343i 0.568310 + 0.235402i
\(22\) 33.4140 26.6589i 1.51882 1.21177i
\(23\) 19.0036 + 19.0036i 0.826244 + 0.826244i 0.986995 0.160751i \(-0.0513916\pi\)
−0.160751 + 0.986995i \(0.551392\pi\)
\(24\) −35.1804 + 16.9708i −1.46585 + 0.707115i
\(25\) 15.9422 + 15.9422i 0.637687 + 0.637687i
\(26\) 0.586128 5.21240i 0.0225434 0.200477i
\(27\) 26.3367 + 10.9090i 0.975434 + 0.404038i
\(28\) −10.3187 2.35037i −0.368525 0.0839420i
\(29\) 23.1121 9.57336i 0.796971 0.330116i 0.0532282 0.998582i \(-0.483049\pi\)
0.743742 + 0.668466i \(0.233049\pi\)
\(30\) 13.3910 + 7.39707i 0.446366 + 0.246569i
\(31\) 12.8494i 0.414497i −0.978288 0.207249i \(-0.933549\pi\)
0.978288 0.207249i \(-0.0664509\pi\)
\(32\) 26.0774 18.5463i 0.814920 0.579573i
\(33\) 104.352 3.16219
\(34\) −22.2400 + 40.2613i −0.654118 + 1.18416i
\(35\) 1.58620 + 3.82944i 0.0453201 + 0.109412i
\(36\) −57.8720 13.1820i −1.60755 0.366166i
\(37\) −17.0724 + 41.2165i −0.461417 + 1.11396i 0.506398 + 0.862300i \(0.330977\pi\)
−0.967816 + 0.251660i \(0.919023\pi\)
\(38\) 60.7448 + 6.83069i 1.59855 + 0.179755i
\(39\) 9.05443 9.05443i 0.232165 0.232165i
\(40\) −11.8326 4.13159i −0.295815 0.103290i
\(41\) 16.4556 16.4556i 0.401357 0.401357i −0.477354 0.878711i \(-0.658404\pi\)
0.878711 + 0.477354i \(0.158404\pi\)
\(42\) −16.1127 20.1955i −0.383636 0.480846i
\(43\) −9.75224 + 23.5440i −0.226796 + 0.547535i −0.995784 0.0917288i \(-0.970761\pi\)
0.768988 + 0.639264i \(0.220761\pi\)
\(44\) −84.2770 + 14.3576i −1.91539 + 0.326309i
\(45\) 8.89615 + 21.4772i 0.197692 + 0.477271i
\(46\) −14.8914 51.6463i −0.323727 1.12275i
\(47\) −40.5701 −0.863194 −0.431597 0.902066i \(-0.642050\pi\)
−0.431597 + 0.902066i \(0.642050\pi\)
\(48\) 78.0006 + 4.31118i 1.62501 + 0.0898162i
\(49\) 7.00000i 0.142857i
\(50\) −12.4924 43.3262i −0.249849 0.866524i
\(51\) −103.739 + 42.9700i −2.03410 + 0.842550i
\(52\) −6.06676 + 8.55832i −0.116669 + 0.164583i
\(53\) −79.5206 32.9385i −1.50039 0.621481i −0.526841 0.849964i \(-0.676624\pi\)
−0.973548 + 0.228483i \(0.926624\pi\)
\(54\) −35.5571 44.5669i −0.658464 0.825313i
\(55\) 23.6765 + 23.6765i 0.430482 + 0.430482i
\(56\) 15.7916 + 14.0934i 0.281993 + 0.251668i
\(57\) 105.519 + 105.519i 1.85122 + 1.85122i
\(58\) −49.7195 5.59090i −0.857232 0.0963948i
\(59\) 61.8251 + 25.6088i 1.04788 + 0.434047i 0.839136 0.543922i \(-0.183061\pi\)
0.208747 + 0.977970i \(0.433061\pi\)
\(60\) −16.2897 25.8995i −0.271496 0.431659i
\(61\) −85.2735 + 35.3215i −1.39793 + 0.579040i −0.949213 0.314635i \(-0.898118\pi\)
−0.448714 + 0.893675i \(0.648118\pi\)
\(62\) −12.4260 + 22.4950i −0.200420 + 0.362822i
\(63\) 39.2592i 0.623161i
\(64\) −63.5880 + 7.25014i −0.993563 + 0.113283i
\(65\) 4.10872 0.0632111
\(66\) −182.685 100.914i −2.76796 1.52900i
\(67\) −7.35639 17.7599i −0.109797 0.265073i 0.859425 0.511262i \(-0.170822\pi\)
−0.969222 + 0.246189i \(0.920822\pi\)
\(68\) 77.8695 48.9767i 1.14514 0.720246i
\(69\) 50.2147 121.229i 0.727749 1.75694i
\(70\) 0.926352 8.23798i 0.0132336 0.117685i
\(71\) −1.36506 + 1.36506i −0.0192262 + 0.0192262i −0.716655 0.697428i \(-0.754328\pi\)
0.697428 + 0.716655i \(0.254328\pi\)
\(72\) 88.5666 + 79.0422i 1.23009 + 1.09781i
\(73\) −30.6133 + 30.6133i −0.419361 + 0.419361i −0.884983 0.465623i \(-0.845830\pi\)
0.465623 + 0.884983i \(0.345830\pi\)
\(74\) 69.7465 55.6462i 0.942520 0.751976i
\(75\) 42.1252 101.699i 0.561669 1.35599i
\(76\) −99.7379 70.7015i −1.31234 0.930283i
\(77\) −21.6397 52.2428i −0.281035 0.678478i
\(78\) −24.6073 + 7.09515i −0.315479 + 0.0909634i
\(79\) −51.5418 −0.652428 −0.326214 0.945296i \(-0.605773\pi\)
−0.326214 + 0.945296i \(0.605773\pi\)
\(80\) 16.7194 + 18.6757i 0.208992 + 0.233446i
\(81\) 5.63591i 0.0695791i
\(82\) −44.7217 + 12.8948i −0.545386 + 0.157254i
\(83\) −16.5575 + 6.85835i −0.199488 + 0.0826307i −0.480191 0.877164i \(-0.659433\pi\)
0.280703 + 0.959795i \(0.409433\pi\)
\(84\) 8.67780 + 50.9374i 0.103307 + 0.606397i
\(85\) −33.2868 13.7878i −0.391609 0.162210i
\(86\) 39.8411 31.7866i 0.463269 0.369612i
\(87\) −86.3674 86.3674i −0.992729 0.992729i
\(88\) 161.425 + 56.3648i 1.83438 + 0.640510i
\(89\) 35.4834 + 35.4834i 0.398690 + 0.398690i 0.877771 0.479081i \(-0.159030\pi\)
−0.479081 + 0.877771i \(0.659030\pi\)
\(90\) 5.19540 46.2023i 0.0577267 0.513359i
\(91\) −6.41063 2.65537i −0.0704464 0.0291799i
\(92\) −23.8748 + 104.816i −0.259508 + 1.13930i
\(93\) −57.9614 + 24.0084i −0.623240 + 0.258155i
\(94\) 71.0245 + 39.2334i 0.755580 + 0.417376i
\(95\) 47.8826i 0.504028i
\(96\) −132.383 82.9779i −1.37899 0.864353i
\(97\) 92.1133 0.949621 0.474811 0.880088i \(-0.342517\pi\)
0.474811 + 0.880088i \(0.342517\pi\)
\(98\) −6.76935 + 12.2546i −0.0690750 + 0.125047i
\(99\) −121.365 293.001i −1.22591 2.95961i
\(100\) −20.0286 + 87.9303i −0.200286 + 0.879303i
\(101\) −38.1862 + 92.1896i −0.378081 + 0.912769i 0.614244 + 0.789116i \(0.289461\pi\)
−0.992326 + 0.123653i \(0.960539\pi\)
\(102\) 223.166 + 25.0947i 2.18790 + 0.246027i
\(103\) −136.832 + 136.832i −1.32847 + 1.32847i −0.421762 + 0.906707i \(0.638588\pi\)
−0.906707 + 0.421762i \(0.861412\pi\)
\(104\) 18.8972 9.11586i 0.181704 0.0876525i
\(105\) 14.3102 14.3102i 0.136287 0.136287i
\(106\) 107.360 + 134.565i 1.01283 + 1.26948i
\(107\) 17.1752 41.4646i 0.160516 0.387520i −0.823075 0.567933i \(-0.807743\pi\)
0.983591 + 0.180413i \(0.0577434\pi\)
\(108\) 19.1499 + 112.407i 0.177314 + 1.04081i
\(109\) 55.3776 + 133.693i 0.508051 + 1.22654i 0.945004 + 0.327059i \(0.106058\pi\)
−0.436953 + 0.899484i \(0.643942\pi\)
\(110\) −18.5531 64.3459i −0.168665 0.584962i
\(111\) 217.819 1.96233
\(112\) −14.0167 39.9441i −0.125149 0.356644i
\(113\) 62.1209i 0.549743i 0.961481 + 0.274871i \(0.0886352\pi\)
−0.961481 + 0.274871i \(0.911365\pi\)
\(114\) −82.6862 286.772i −0.725317 2.51554i
\(115\) 38.8989 16.1124i 0.338251 0.140108i
\(116\) 81.6352 + 57.8690i 0.703752 + 0.498871i
\(117\) −35.9537 14.8925i −0.307296 0.127286i
\(118\) −83.4698 104.620i −0.707371 0.886612i
\(119\) 43.0249 + 43.0249i 0.361554 + 0.361554i
\(120\) 3.47166 + 61.0943i 0.0289305 + 0.509119i
\(121\) −237.445 237.445i −1.96235 1.96235i
\(122\) 183.443 + 20.6279i 1.50363 + 0.169081i
\(123\) −104.975 43.4820i −0.853454 0.353512i
\(124\) 43.5075 27.3644i 0.350867 0.220681i
\(125\) 68.8171 28.5050i 0.550537 0.228040i
\(126\) −37.9656 + 68.7295i −0.301314 + 0.545472i
\(127\) 173.646i 1.36729i −0.729813 0.683647i \(-0.760393\pi\)
0.729813 0.683647i \(-0.239607\pi\)
\(128\) 118.332 + 48.8003i 0.924471 + 0.381252i
\(129\) 124.424 0.964529
\(130\) −7.19298 3.97334i −0.0553306 0.0305642i
\(131\) −0.0398470 0.0961992i −0.000304176 0.000734345i 0.923727 0.383051i \(-0.125127\pi\)
−0.924032 + 0.382316i \(0.875127\pi\)
\(132\) 222.231 + 353.332i 1.68357 + 2.67676i
\(133\) 30.9454 74.7088i 0.232672 0.561721i
\(134\) −4.29617 + 38.2056i −0.0320610 + 0.285116i
\(135\) 31.5792 31.5792i 0.233920 0.233920i
\(136\) −183.686 + 10.4379i −1.35063 + 0.0767492i
\(137\) −96.9345 + 96.9345i −0.707551 + 0.707551i −0.966020 0.258469i \(-0.916782\pi\)
0.258469 + 0.966020i \(0.416782\pi\)
\(138\) −205.144 + 163.671i −1.48655 + 1.18602i
\(139\) −28.0338 + 67.6795i −0.201682 + 0.486903i −0.992067 0.125707i \(-0.959880\pi\)
0.790386 + 0.612609i \(0.209880\pi\)
\(140\) −9.58827 + 13.5261i −0.0684877 + 0.0966149i
\(141\) 75.8029 + 183.004i 0.537610 + 1.29790i
\(142\) 3.70984 1.06968i 0.0261256 0.00753293i
\(143\) −56.0529 −0.391978
\(144\) −78.6122 224.024i −0.545918 1.55573i
\(145\) 39.1918i 0.270288i
\(146\) 83.1982 23.9889i 0.569851 0.164308i
\(147\) −31.5757 + 13.0791i −0.214801 + 0.0889734i
\(148\) −175.915 + 29.9693i −1.18862 + 0.202495i
\(149\) 76.1578 + 31.5456i 0.511126 + 0.211715i 0.623314 0.781972i \(-0.285786\pi\)
−0.112188 + 0.993687i \(0.535786\pi\)
\(150\) −172.095 + 137.304i −1.14730 + 0.915358i
\(151\) −72.4734 72.4734i −0.479956 0.479956i 0.425161 0.905118i \(-0.360217\pi\)
−0.905118 + 0.425161i \(0.860217\pi\)
\(152\) 106.235 + 220.226i 0.698917 + 1.44886i
\(153\) 241.303 + 241.303i 1.57714 + 1.57714i
\(154\) −12.6377 + 112.386i −0.0820629 + 0.729779i
\(155\) −18.5981 7.70359i −0.119988 0.0497006i
\(156\) 49.9404 + 11.3753i 0.320131 + 0.0729188i
\(157\) −86.4063 + 35.7907i −0.550359 + 0.227966i −0.640494 0.767964i \(-0.721270\pi\)
0.0901348 + 0.995930i \(0.471270\pi\)
\(158\) 90.2323 + 49.8436i 0.571090 + 0.315466i
\(159\) 420.247i 2.64306i
\(160\) −11.2096 48.8633i −0.0700601 0.305396i
\(161\) −71.1050 −0.441646
\(162\) −5.45021 + 9.86657i −0.0336433 + 0.0609047i
\(163\) −13.3359 32.1956i −0.0818152 0.197519i 0.877678 0.479250i \(-0.159091\pi\)
−0.959493 + 0.281731i \(0.909091\pi\)
\(164\) 90.7624 + 20.6737i 0.553429 + 0.126059i
\(165\) 62.5622 151.039i 0.379165 0.915385i
\(166\) 35.6190 + 4.00531i 0.214572 + 0.0241284i
\(167\) 22.3201 22.3201i 0.133653 0.133653i −0.637115 0.770769i \(-0.719872\pi\)
0.770769 + 0.637115i \(0.219872\pi\)
\(168\) 34.0671 97.5659i 0.202780 0.580749i
\(169\) 114.637 114.637i 0.678328 0.678328i
\(170\) 44.9403 + 56.3278i 0.264355 + 0.331340i
\(171\) 173.556 419.001i 1.01495 2.45030i
\(172\) −100.488 + 17.1193i −0.584230 + 0.0995306i
\(173\) −60.7590 146.685i −0.351208 0.847891i −0.996472 0.0839310i \(-0.973252\pi\)
0.645264 0.763960i \(-0.276748\pi\)
\(174\) 67.6784 + 234.722i 0.388956 + 1.34898i
\(175\) −59.6501 −0.340858
\(176\) −228.093 254.782i −1.29598 1.44762i
\(177\) 326.730i 1.84593i
\(178\) −27.8052 96.4337i −0.156209 0.541762i
\(179\) −53.5376 + 22.1760i −0.299093 + 0.123888i −0.527183 0.849752i \(-0.676752\pi\)
0.228091 + 0.973640i \(0.426752\pi\)
\(180\) −53.7754 + 75.8604i −0.298752 + 0.421447i
\(181\) −99.2966 41.1300i −0.548600 0.227238i 0.0911277 0.995839i \(-0.470953\pi\)
−0.639728 + 0.768602i \(0.720953\pi\)
\(182\) 8.65496 + 10.8480i 0.0475547 + 0.0596047i
\(183\) 318.657 + 318.657i 1.74130 + 1.74130i
\(184\) 143.159 160.409i 0.778038 0.871789i
\(185\) 49.4210 + 49.4210i 0.267141 + 0.267141i
\(186\) 124.688 + 14.0210i 0.670366 + 0.0753819i
\(187\) 454.112 + 188.100i 2.42841 + 1.00588i
\(188\) −86.3992 137.369i −0.459570 0.730684i
\(189\) −69.6804 + 28.8626i −0.368679 + 0.152712i
\(190\) 46.3049 83.8263i 0.243710 0.441191i
\(191\) 1.12694i 0.00590023i 0.999996 + 0.00295011i \(0.000939052\pi\)
−0.999996 + 0.00295011i \(0.999061\pi\)
\(192\) 151.515 + 273.288i 0.789139 + 1.42337i
\(193\) 202.020 1.04673 0.523367 0.852108i \(-0.324676\pi\)
0.523367 + 0.852108i \(0.324676\pi\)
\(194\) −161.259 89.0782i −0.831232 0.459166i
\(195\) −7.67691 18.5337i −0.0393688 0.0950446i
\(196\) 23.7017 14.9074i 0.120927 0.0760581i
\(197\) 47.2681 114.115i 0.239939 0.579265i −0.757337 0.653025i \(-0.773500\pi\)
0.997276 + 0.0737598i \(0.0234998\pi\)
\(198\) −70.8778 + 630.311i −0.357969 + 3.18339i
\(199\) −21.7553 + 21.7553i −0.109323 + 0.109323i −0.759652 0.650329i \(-0.774631\pi\)
0.650329 + 0.759652i \(0.274631\pi\)
\(200\) 120.096 134.567i 0.600482 0.672837i
\(201\) −66.3667 + 66.3667i −0.330183 + 0.330183i
\(202\) 156.003 124.465i 0.772293 0.616162i
\(203\) −25.3287 + 61.1490i −0.124772 + 0.301227i
\(204\) −366.420 259.745i −1.79618 1.27326i
\(205\) −13.9521 33.6834i −0.0680591 0.164309i
\(206\) 371.871 107.223i 1.80520 0.520501i
\(207\) −398.789 −1.92652
\(208\) −41.8980 2.31575i −0.201433 0.0111334i
\(209\) 653.235i 3.12553i
\(210\) −38.8909 + 11.2136i −0.185195 + 0.0533980i
\(211\) −70.9017 + 29.3685i −0.336027 + 0.139187i −0.544316 0.838880i \(-0.683211\pi\)
0.208289 + 0.978067i \(0.433211\pi\)
\(212\) −57.8209 339.400i −0.272740 1.60094i
\(213\) 8.70808 + 3.60700i 0.0408830 + 0.0169343i
\(214\) −70.1663 + 55.9812i −0.327880 + 0.261594i
\(215\) 28.2306 + 28.2306i 0.131305 + 0.131305i
\(216\) 75.1783 215.306i 0.348048 0.996785i
\(217\) 24.0390 + 24.0390i 0.110779 + 0.110779i
\(218\) 32.3408 287.604i 0.148352 1.31929i
\(219\) 195.290 + 80.8919i 0.891737 + 0.369370i
\(220\) −29.7454 + 130.590i −0.135207 + 0.593589i
\(221\) 55.7234 23.0814i 0.252142 0.104441i
\(222\) −381.327 210.642i −1.71769 0.948838i
\(223\) 274.273i 1.22993i 0.788556 + 0.614963i \(0.210829\pi\)
−0.788556 + 0.614963i \(0.789171\pi\)
\(224\) −14.0894 + 83.4835i −0.0628992 + 0.372694i
\(225\) −334.545 −1.48687
\(226\) 60.0741 108.753i 0.265814 0.481206i
\(227\) −88.8946 214.611i −0.391606 0.945421i −0.989590 0.143913i \(-0.954031\pi\)
0.597984 0.801508i \(-0.295969\pi\)
\(228\) −132.567 + 582.001i −0.581435 + 2.55264i
\(229\) 26.8397 64.7967i 0.117204 0.282955i −0.854381 0.519647i \(-0.826063\pi\)
0.971585 + 0.236692i \(0.0760633\pi\)
\(230\) −83.6803 9.40976i −0.363827 0.0409120i
\(231\) −195.225 + 195.225i −0.845131 + 0.845131i
\(232\) −86.9534 180.254i −0.374799 0.776958i
\(233\) 23.8805 23.8805i 0.102492 0.102492i −0.654002 0.756493i \(-0.726911\pi\)
0.756493 + 0.654002i \(0.226911\pi\)
\(234\) 48.5409 + 60.8407i 0.207440 + 0.260003i
\(235\) −24.3230 + 58.7208i −0.103502 + 0.249876i
\(236\) 44.9541 + 263.874i 0.190484 + 1.11811i
\(237\) 96.3030 + 232.496i 0.406342 + 0.980995i
\(238\) −33.7148 116.929i −0.141659 0.491300i
\(239\) −362.213 −1.51554 −0.757768 0.652524i \(-0.773710\pi\)
−0.757768 + 0.652524i \(0.773710\pi\)
\(240\) 53.0035 110.313i 0.220848 0.459636i
\(241\) 168.533i 0.699307i 0.936879 + 0.349654i \(0.113701\pi\)
−0.936879 + 0.349654i \(0.886299\pi\)
\(242\) 186.064 + 645.306i 0.768860 + 2.66656i
\(243\) 211.608 87.6508i 0.870814 0.360703i
\(244\) −301.198 213.511i −1.23442 0.875044i
\(245\) −10.1317 4.19670i −0.0413540 0.0171294i
\(246\) 141.726 + 177.638i 0.576122 + 0.722106i
\(247\) −56.6799 56.6799i −0.229473 0.229473i
\(248\) −102.630 + 5.83190i −0.413830 + 0.0235157i
\(249\) 61.8735 + 61.8735i 0.248488 + 0.248488i
\(250\) −148.041 16.6471i −0.592165 0.0665883i
\(251\) −388.164 160.783i −1.54647 0.640569i −0.563796 0.825914i \(-0.690660\pi\)
−0.982673 + 0.185345i \(0.940660\pi\)
\(252\) 132.930 83.6073i 0.527499 0.331775i
\(253\) −530.675 + 219.813i −2.09753 + 0.868825i
\(254\) −167.925 + 303.996i −0.661121 + 1.19683i
\(255\) 175.912i 0.689853i
\(256\) −159.967 199.866i −0.624873 0.780727i
\(257\) −46.7470 −0.181895 −0.0909475 0.995856i \(-0.528990\pi\)
−0.0909475 + 0.995856i \(0.528990\pi\)
\(258\) −217.825 120.324i −0.844281 0.466374i
\(259\) −45.1694 109.049i −0.174399 0.421037i
\(260\) 8.75004 + 13.9119i 0.0336540 + 0.0535075i
\(261\) −142.055 + 342.951i −0.544272 + 1.31399i
\(262\) −0.0232709 + 0.206946i −8.88202e−5 + 0.000789872i
\(263\) 267.611 267.611i 1.01753 1.01753i 0.0176891 0.999844i \(-0.494369\pi\)
0.999844 0.0176891i \(-0.00563091\pi\)
\(264\) −47.3618 833.474i −0.179401 3.15710i
\(265\) −95.3498 + 95.3498i −0.359811 + 0.359811i
\(266\) −126.422 + 100.864i −0.475271 + 0.379188i
\(267\) 93.7606 226.358i 0.351163 0.847783i
\(268\) 44.4679 62.7304i 0.165925 0.234069i
\(269\) −170.756 412.242i −0.634782 1.53250i −0.833545 0.552451i \(-0.813693\pi\)
0.198764 0.980047i \(-0.436307\pi\)
\(270\) −85.8232 + 24.7458i −0.317864 + 0.0916512i
\(271\) 311.278 1.14863 0.574314 0.818635i \(-0.305269\pi\)
0.574314 + 0.818635i \(0.305269\pi\)
\(272\) 331.666 + 159.360i 1.21936 + 0.585884i
\(273\) 33.8786i 0.124097i
\(274\) 263.440 75.9589i 0.961460 0.277222i
\(275\) −445.184 + 184.401i −1.61885 + 0.670550i
\(276\) 517.415 88.1478i 1.87469 0.319376i
\(277\) −231.786 96.0091i −0.836774 0.346603i −0.0771934 0.997016i \(-0.524596\pi\)
−0.759581 + 0.650413i \(0.774596\pi\)
\(278\) 114.527 91.3737i 0.411968 0.328683i
\(279\) 134.822 + 134.822i 0.483232 + 0.483232i
\(280\) 29.8662 14.4072i 0.106665 0.0514544i
\(281\) 174.086 + 174.086i 0.619523 + 0.619523i 0.945409 0.325886i \(-0.105663\pi\)
−0.325886 + 0.945409i \(0.605663\pi\)
\(282\) 44.2693 393.684i 0.156983 1.39604i
\(283\) 188.518 + 78.0865i 0.666140 + 0.275924i 0.690020 0.723791i \(-0.257602\pi\)
−0.0238797 + 0.999715i \(0.507602\pi\)
\(284\) −7.52910 1.71496i −0.0265109 0.00603861i
\(285\) 215.990 89.4660i 0.757859 0.313916i
\(286\) 98.1296 + 54.2060i 0.343110 + 0.189531i
\(287\) 61.5713i 0.214534i
\(288\) −79.0198 + 468.213i −0.274374 + 1.62574i
\(289\) −239.898 −0.830098
\(290\) −37.9005 + 68.6116i −0.130691 + 0.236592i
\(291\) −172.108 415.506i −0.591438 1.42786i
\(292\) −168.850 38.4604i −0.578254 0.131714i
\(293\) 36.3025 87.6421i 0.123899 0.299120i −0.849744 0.527196i \(-0.823243\pi\)
0.973643 + 0.228076i \(0.0732435\pi\)
\(294\) 67.9265 + 7.63827i 0.231043 + 0.0259805i
\(295\) 74.1318 74.1318i 0.251294 0.251294i
\(296\) 336.950 + 117.653i 1.13834 + 0.397476i
\(297\) −430.817 + 430.817i −1.45056 + 1.45056i
\(298\) −102.820 128.874i −0.345034 0.432463i
\(299\) −26.9729 + 65.1182i −0.0902102 + 0.217787i
\(300\) 434.060 73.9474i 1.44687 0.246491i
\(301\) −25.8020 62.2916i −0.0857209 0.206949i
\(302\) 56.7909 + 196.962i 0.188049 + 0.652191i
\(303\) 487.199 1.60792
\(304\) 26.9875 488.276i 0.0887748 1.60617i
\(305\) 144.600i 0.474100i
\(306\) −189.088 655.792i −0.617934 2.14311i
\(307\) 351.286 145.508i 1.14425 0.473966i 0.271652 0.962396i \(-0.412430\pi\)
0.872603 + 0.488430i \(0.162430\pi\)
\(308\) 130.807 184.529i 0.424699 0.599119i
\(309\) 872.889 + 361.562i 2.82488 + 1.17010i
\(310\) 25.1092 + 31.4717i 0.0809975 + 0.101522i
\(311\) −14.9495 14.9495i −0.0480691 0.0480691i 0.682664 0.730733i \(-0.260821\pi\)
−0.730733 + 0.682664i \(0.760821\pi\)
\(312\) −76.4283 68.2093i −0.244962 0.218620i
\(313\) 44.1343 + 44.1343i 0.141004 + 0.141004i 0.774085 0.633081i \(-0.218210\pi\)
−0.633081 + 0.774085i \(0.718210\pi\)
\(314\) 185.880 + 20.9020i 0.591973 + 0.0665667i
\(315\) −56.8233 23.5370i −0.180392 0.0747206i
\(316\) −109.765 174.518i −0.347357 0.552273i
\(317\) −401.013 + 166.105i −1.26502 + 0.523990i −0.911448 0.411415i \(-0.865035\pi\)
−0.353577 + 0.935406i \(0.615035\pi\)
\(318\) 406.400 735.710i 1.27799 2.31355i
\(319\) 534.671i 1.67609i
\(320\) −27.6291 + 96.3834i −0.0863408 + 0.301198i
\(321\) −219.130 −0.682649
\(322\) 124.481 + 68.7621i 0.386586 + 0.213547i
\(323\) 268.988 + 649.395i 0.832781 + 2.01051i
\(324\) 19.0829 12.0024i 0.0588980 0.0370444i
\(325\) −22.6276 + 54.6278i −0.0696233 + 0.168086i
\(326\) −7.78822 + 69.2601i −0.0238903 + 0.212454i
\(327\) 499.596 499.596i 1.52782 1.52782i
\(328\) −138.902 123.964i −0.423481 0.377940i
\(329\) 75.8998 75.8998i 0.230698 0.230698i
\(330\) −255.587 + 203.916i −0.774506 + 0.617929i
\(331\) 47.5098 114.699i 0.143534 0.346522i −0.835721 0.549155i \(-0.814950\pi\)
0.979255 + 0.202633i \(0.0649498\pi\)
\(332\) −58.4834 41.4573i −0.176155 0.124871i
\(333\) −253.331 611.594i −0.760752 1.83662i
\(334\) −60.6597 + 17.4903i −0.181616 + 0.0523661i
\(335\) −30.1159 −0.0898982
\(336\) −153.991 + 137.860i −0.458307 + 0.410298i
\(337\) 121.817i 0.361473i −0.983532 0.180737i \(-0.942152\pi\)
0.983532 0.180737i \(-0.0578482\pi\)
\(338\) −311.552 + 89.8311i −0.921750 + 0.265772i
\(339\) 280.216 116.069i 0.826596 0.342387i
\(340\) −24.2034 142.071i −0.0711866 0.417854i
\(341\) 253.723 + 105.096i 0.744057 + 0.308198i
\(342\) −709.032 + 565.691i −2.07319 + 1.65407i
\(343\) 13.0958 + 13.0958i 0.0381802 + 0.0381802i
\(344\) 192.475 + 67.2065i 0.559520 + 0.195368i
\(345\) −145.361 145.361i −0.421335 0.421335i
\(346\) −35.4836 + 315.553i −0.102554 + 0.912003i
\(347\) 574.616 + 238.014i 1.65595 + 0.685919i 0.997758 0.0669278i \(-0.0213197\pi\)
0.658196 + 0.752846i \(0.271320\pi\)
\(348\) 108.506 476.367i 0.311798 1.36887i
\(349\) −513.357 + 212.639i −1.47094 + 0.609282i −0.967073 0.254501i \(-0.918089\pi\)
−0.503865 + 0.863783i \(0.668089\pi\)
\(350\) 104.427 + 57.6847i 0.298363 + 0.164813i
\(351\) 74.7622i 0.212998i
\(352\) 152.926 + 666.614i 0.434450 + 1.89379i
\(353\) −294.021 −0.832921 −0.416461 0.909154i \(-0.636730\pi\)
−0.416461 + 0.909154i \(0.636730\pi\)
\(354\) −315.965 + 571.994i −0.892556 + 1.61580i
\(355\) 1.15738 + 2.79417i 0.00326023 + 0.00787090i
\(356\) −44.5788 + 195.712i −0.125221 + 0.549752i
\(357\) 113.688 274.467i 0.318454 0.768816i
\(358\) 115.171 + 12.9509i 0.321708 + 0.0361757i
\(359\) 204.988 204.988i 0.570998 0.570998i −0.361409 0.932407i \(-0.617704\pi\)
0.932407 + 0.361409i \(0.117704\pi\)
\(360\) 167.503 80.8023i 0.465287 0.224451i
\(361\) 405.276 405.276i 1.12265 1.12265i
\(362\) 134.060 + 168.029i 0.370331 + 0.464170i
\(363\) −627.418 + 1514.72i −1.72843 + 4.17279i
\(364\) −4.66128 27.3610i −0.0128057 0.0751677i
\(365\) 25.9559 + 62.6630i 0.0711120 + 0.171680i
\(366\) −249.703 866.019i −0.682249 2.36617i
\(367\) 381.654 1.03993 0.519964 0.854188i \(-0.325945\pi\)
0.519964 + 0.854188i \(0.325945\pi\)
\(368\) −405.747 + 142.380i −1.10257 + 0.386902i
\(369\) 345.320i 0.935826i
\(370\) −38.7268 134.312i −0.104667 0.363005i
\(371\) 210.392 87.1471i 0.567094 0.234898i
\(372\) −204.727 145.126i −0.550342 0.390123i
\(373\) 622.072 + 257.671i 1.66775 + 0.690806i 0.998629 0.0523442i \(-0.0166693\pi\)
0.669124 + 0.743150i \(0.266669\pi\)
\(374\) −613.095 768.448i −1.63929 2.05467i
\(375\) −257.162 257.162i −0.685764 0.685764i
\(376\) 18.4134 + 324.038i 0.0489717 + 0.861804i
\(377\) 46.3923 + 46.3923i 0.123057 + 0.123057i
\(378\) 149.898 + 16.8559i 0.396556 + 0.0445923i
\(379\) −224.045 92.8025i −0.591148 0.244861i 0.0669966 0.997753i \(-0.478658\pi\)
−0.658144 + 0.752892i \(0.728658\pi\)
\(380\) −162.128 + 101.972i −0.426654 + 0.268348i
\(381\) −783.287 + 324.448i −2.05587 + 0.851570i
\(382\) 1.08981 1.97290i 0.00285291 0.00516465i
\(383\) 124.986i 0.326334i 0.986598 + 0.163167i \(0.0521710\pi\)
−0.986598 + 0.163167i \(0.947829\pi\)
\(384\) −0.967849 624.956i −0.00252044 1.62749i
\(385\) −88.5893 −0.230102
\(386\) −353.668 195.363i −0.916238 0.506122i
\(387\) −144.709 349.359i −0.373926 0.902737i
\(388\) 196.167 + 311.891i 0.505585 + 0.803844i
\(389\) −70.1154 + 169.274i −0.180245 + 0.435151i −0.988017 0.154345i \(-0.950673\pi\)
0.807772 + 0.589495i \(0.200673\pi\)
\(390\) −4.48336 + 39.8702i −0.0114958 + 0.102231i
\(391\) 437.041 437.041i 1.11775 1.11775i
\(392\) −55.9098 + 3.17705i −0.142627 + 0.00810473i
\(393\) −0.359485 + 0.359485i −0.000914721 + 0.000914721i
\(394\) −193.105 + 154.066i −0.490115 + 0.391031i
\(395\) −30.9008 + 74.6012i −0.0782299 + 0.188864i
\(396\) 733.626 1034.92i 1.85259 2.61343i
\(397\) −48.4366 116.936i −0.122007 0.294550i 0.851062 0.525065i \(-0.175959\pi\)
−0.973069 + 0.230515i \(0.925959\pi\)
\(398\) 59.1246 17.0477i 0.148554 0.0428334i
\(399\) −394.818 −0.989518
\(400\) −340.381 + 119.443i −0.850954 + 0.298607i
\(401\) 174.952i 0.436289i 0.975916 + 0.218145i \(0.0700005\pi\)
−0.975916 + 0.218145i \(0.930000\pi\)
\(402\) 180.366 52.0056i 0.448671 0.129367i
\(403\) 31.1340 12.8961i 0.0772555 0.0320003i
\(404\) −393.472 + 67.0328i −0.973941 + 0.165923i
\(405\) −8.15736 3.37889i −0.0201416 0.00834294i
\(406\) 103.476 82.5570i 0.254867 0.203342i
\(407\) −674.222 674.222i −1.65657 1.65657i
\(408\) 390.290 + 809.072i 0.956594 + 1.98302i
\(409\) 528.452 + 528.452i 1.29206 + 1.29206i 0.933512 + 0.358545i \(0.116727\pi\)
0.358545 + 0.933512i \(0.383273\pi\)
\(410\) −8.14811 + 72.4605i −0.0198734 + 0.176733i
\(411\) 618.370 + 256.137i 1.50455 + 0.623205i
\(412\) −754.709 171.906i −1.83182 0.417248i
\(413\) −163.574 + 67.7545i −0.396062 + 0.164054i
\(414\) 698.144 + 385.649i 1.68634 + 0.931519i
\(415\) 28.0770i 0.0676554i
\(416\) 71.1098 + 44.5716i 0.170937 + 0.107143i
\(417\) 357.669 0.857720
\(418\) −631.711 + 1143.59i −1.51127 + 2.73587i
\(419\) 188.347 + 454.710i 0.449516 + 1.08523i 0.972504 + 0.232888i \(0.0748174\pi\)
−0.522988 + 0.852340i \(0.675183\pi\)
\(420\) 78.9289 + 17.9783i 0.187926 + 0.0428054i
\(421\) −61.6928 + 148.940i −0.146539 + 0.353776i −0.980057 0.198716i \(-0.936323\pi\)
0.833518 + 0.552492i \(0.186323\pi\)
\(422\) 152.526 + 17.1513i 0.361435 + 0.0406430i
\(423\) 425.680 425.680i 1.00634 1.00634i
\(424\) −226.992 + 650.090i −0.535359 + 1.53323i
\(425\) 366.635 366.635i 0.862670 0.862670i
\(426\) −11.7567 14.7358i −0.0275980 0.0345911i
\(427\) 93.4518 225.613i 0.218857 0.528367i
\(428\) 176.974 30.1497i 0.413491 0.0704432i
\(429\) 104.732 + 252.844i 0.244130 + 0.589381i
\(430\) −22.1218 76.7226i −0.0514460 0.178425i
\(431\) −215.252 −0.499424 −0.249712 0.968320i \(-0.580336\pi\)
−0.249712 + 0.968320i \(0.580336\pi\)
\(432\) −339.823 + 304.226i −0.786627 + 0.704226i
\(433\) 366.404i 0.846199i 0.906083 + 0.423099i \(0.139058\pi\)
−0.906083 + 0.423099i \(0.860942\pi\)
\(434\) −18.8372 65.3312i −0.0434038 0.150533i
\(435\) −176.787 + 73.2277i −0.406407 + 0.168339i
\(436\) −334.746 + 472.223i −0.767765 + 1.08308i
\(437\) −758.882 314.339i −1.73657 0.719312i
\(438\) −263.661 330.470i −0.601965 0.754498i
\(439\) −339.246 339.246i −0.772769 0.772769i 0.205821 0.978590i \(-0.434014\pi\)
−0.978590 + 0.205821i \(0.934014\pi\)
\(440\) 178.361 199.853i 0.405366 0.454211i
\(441\) 73.4471 + 73.4471i 0.166547 + 0.166547i
\(442\) −119.874 13.4797i −0.271207 0.0304970i
\(443\) −281.942 116.784i −0.636438 0.263621i 0.0410474 0.999157i \(-0.486931\pi\)
−0.677486 + 0.735536i \(0.736931\pi\)
\(444\) 463.873 + 737.526i 1.04476 + 1.66109i
\(445\) 72.6317 30.0850i 0.163217 0.0676068i
\(446\) 265.236 480.160i 0.594700 1.07659i
\(447\) 402.475i 0.900392i
\(448\) 105.399 132.526i 0.235265 0.295817i
\(449\) 153.549 0.341979 0.170990 0.985273i \(-0.445304\pi\)
0.170990 + 0.985273i \(0.445304\pi\)
\(450\) 585.674 + 323.522i 1.30150 + 0.718937i
\(451\) 190.341 + 459.523i 0.422041 + 1.01890i
\(452\) −210.339 + 132.294i −0.465351 + 0.292687i
\(453\) −191.502 + 462.327i −0.422742 + 1.02059i
\(454\) −51.9150 + 461.676i −0.114350 + 1.01691i
\(455\) −7.68671 + 7.68671i −0.0168939 + 0.0168939i
\(456\) 794.905 890.688i 1.74321 1.95326i
\(457\) 439.797 439.797i 0.962357 0.962357i −0.0369598 0.999317i \(-0.511767\pi\)
0.999317 + 0.0369598i \(0.0117674\pi\)
\(458\) −109.649 + 87.4818i −0.239408 + 0.191008i
\(459\) 250.883 605.686i 0.546587 1.31958i
\(460\) 137.396 + 97.3963i 0.298687 + 0.211731i
\(461\) −25.1877 60.8086i −0.0546372 0.131906i 0.894204 0.447660i \(-0.147743\pi\)
−0.948841 + 0.315754i \(0.897743\pi\)
\(462\) 530.566 152.981i 1.14841 0.331127i
\(463\) 477.910 1.03220 0.516102 0.856527i \(-0.327383\pi\)
0.516102 + 0.856527i \(0.327383\pi\)
\(464\) −22.0892 + 399.653i −0.0476061 + 0.861320i
\(465\) 98.2865i 0.211369i
\(466\) −64.9004 + 18.7130i −0.139271 + 0.0401567i
\(467\) −70.1971 + 29.0766i −0.150315 + 0.0622625i −0.456573 0.889686i \(-0.650923\pi\)
0.306258 + 0.951949i \(0.400923\pi\)
\(468\) −26.1426 153.453i −0.0558602 0.327891i
\(469\) 46.9883 + 19.4632i 0.100188 + 0.0414993i
\(470\) 99.3673 79.2787i 0.211420 0.168678i
\(471\) 322.890 + 322.890i 0.685542 + 0.685542i
\(472\) 176.480 505.427i 0.373898 1.07082i
\(473\) −385.134 385.134i −0.814236 0.814236i
\(474\) 56.2415 500.151i 0.118653 1.05517i
\(475\) −636.627 263.700i −1.34027 0.555157i
\(476\) −54.0534 + 237.308i −0.113558 + 0.498545i
\(477\) 1179.97 488.760i 2.47373 1.02465i
\(478\) 634.113 + 350.279i 1.32660 + 0.732800i
\(479\) 282.395i 0.589551i −0.955566 0.294776i \(-0.904755\pi\)
0.955566 0.294776i \(-0.0952449\pi\)
\(480\) −199.469 + 141.863i −0.415561 + 0.295548i
\(481\) −117.002 −0.243247
\(482\) 162.980 295.044i 0.338133 0.612125i
\(483\) 132.856 + 320.742i 0.275063 + 0.664062i
\(484\) 298.309 1309.65i 0.616340 2.70588i
\(485\) 55.2246 133.324i 0.113865 0.274895i
\(486\) −455.216 51.1886i −0.936659 0.105326i
\(487\) −116.858 + 116.858i −0.239955 + 0.239955i −0.816832 0.576876i \(-0.804271\pi\)
0.576876 + 0.816832i \(0.304271\pi\)
\(488\) 320.819 + 665.058i 0.657416 + 1.36282i
\(489\) −120.311 + 120.311i −0.246036 + 0.246036i
\(490\) 13.6788 + 17.1449i 0.0279159 + 0.0349896i
\(491\) −278.878 + 673.270i −0.567979 + 1.37122i 0.335277 + 0.942120i \(0.391170\pi\)
−0.903256 + 0.429102i \(0.858830\pi\)
\(492\) −76.3291 448.040i −0.155140 0.910651i
\(493\) −220.166 531.528i −0.446585 1.07815i
\(494\) 44.4149 + 154.039i 0.0899088 + 0.311821i
\(495\) −496.849 −1.00373
\(496\) 185.310 + 89.0384i 0.373608 + 0.179513i
\(497\) 5.10759i 0.0102768i
\(498\) −48.4847 168.154i −0.0973589 0.337659i
\(499\) −249.439 + 103.321i −0.499878 + 0.207056i −0.618352 0.785901i \(-0.712200\pi\)
0.118475 + 0.992957i \(0.462200\pi\)
\(500\) 243.071 + 172.307i 0.486143 + 0.344613i
\(501\) −142.386 58.9782i −0.284204 0.117721i
\(502\) 524.058 + 656.850i 1.04394 + 1.30847i
\(503\) −428.032 428.032i −0.850959 0.850959i 0.139293 0.990251i \(-0.455517\pi\)
−0.990251 + 0.139293i \(0.955517\pi\)
\(504\) −313.567 + 17.8183i −0.622157 + 0.0353539i
\(505\) 110.541 + 110.541i 0.218892 + 0.218892i
\(506\) 1141.60 + 128.372i 2.25613 + 0.253699i
\(507\) −731.302 302.915i −1.44241 0.597466i
\(508\) 587.959 369.802i 1.15740 0.727957i
\(509\) 748.679 310.113i 1.47088 0.609259i 0.503822 0.863808i \(-0.331927\pi\)
0.967060 + 0.254548i \(0.0819268\pi\)
\(510\) 170.116 307.963i 0.333561 0.603849i
\(511\) 114.545i 0.224158i
\(512\) 86.7681 + 504.594i 0.169469 + 0.985536i
\(513\) −871.272 −1.69839
\(514\) 81.8382 + 45.2067i 0.159218 + 0.0879508i
\(515\) 116.015 + 280.085i 0.225272 + 0.543854i
\(516\) 264.977 + 421.295i 0.513521 + 0.816463i
\(517\) 331.824 801.094i 0.641826 1.54951i
\(518\) −26.3792 + 234.588i −0.0509251 + 0.452873i
\(519\) −548.145 + 548.145i −1.05616 + 1.05616i
\(520\) −1.86480 32.8168i −0.00358616 0.0631093i
\(521\) −369.061 + 369.061i −0.708370 + 0.708370i −0.966192 0.257822i \(-0.916995\pi\)
0.257822 + 0.966192i \(0.416995\pi\)
\(522\) 580.341 463.017i 1.11176 0.887005i
\(523\) −27.7801 + 67.0672i −0.0531169 + 0.128236i −0.948210 0.317643i \(-0.897109\pi\)
0.895093 + 0.445878i \(0.147109\pi\)
\(524\) 0.240867 0.339789i 0.000459670 0.000648452i
\(525\) 111.453 + 269.071i 0.212291 + 0.512516i
\(526\) −727.290 + 209.703i −1.38268 + 0.398675i
\(527\) −295.508 −0.560736
\(528\) −723.097 + 1504.93i −1.36950 + 2.85025i
\(529\) 193.275i 0.365359i
\(530\) 259.133 74.7171i 0.488931 0.140976i
\(531\) −917.395 + 379.998i −1.72767 + 0.715626i
\(532\) 318.863 54.3222i 0.599366 0.102109i
\(533\) 56.3873 + 23.3564i 0.105792 + 0.0438206i
\(534\) −383.043 + 305.605i −0.717308 + 0.572294i
\(535\) −49.7185 49.7185i −0.0929317 0.0929317i
\(536\) −138.512 + 66.8169i −0.258417 + 0.124658i
\(537\) 200.064 + 200.064i 0.372558 + 0.372558i
\(538\) −99.7226 + 886.826i −0.185358 + 1.64838i
\(539\) 138.221 + 57.2532i 0.256440 + 0.106221i
\(540\) 174.178 + 39.6739i 0.322552 + 0.0734701i
\(541\) 252.250 104.485i 0.466266 0.193134i −0.137166 0.990548i \(-0.543799\pi\)
0.603432 + 0.797414i \(0.293799\pi\)
\(542\) −544.942 301.022i −1.00543 0.555390i
\(543\) 524.758i 0.966405i
\(544\) −426.525 599.724i −0.784053 1.10243i
\(545\) 226.707 0.415976
\(546\) 32.7623 59.3099i 0.0600042 0.108626i
\(547\) −73.3465 177.074i −0.134089 0.323719i 0.842546 0.538624i \(-0.181056\pi\)
−0.976635 + 0.214905i \(0.931056\pi\)
\(548\) −534.650 121.782i −0.975639 0.222229i
\(549\) 524.120 1265.34i 0.954681 2.30480i
\(550\) 957.691 + 107.691i 1.74126 + 0.195802i
\(551\) −540.652 + 540.652i −0.981219 + 0.981219i
\(552\) −991.061 346.049i −1.79540 0.626900i
\(553\) 96.4259 96.4259i 0.174369 0.174369i
\(554\) 312.934 + 392.229i 0.564863 + 0.707994i
\(555\) 130.589 315.269i 0.235295 0.568053i
\(556\) −288.861 + 49.2110i −0.519534 + 0.0885090i
\(557\) −300.789 726.170i −0.540017 1.30372i −0.924710 0.380671i \(-0.875693\pi\)
0.384694 0.923044i \(-0.374307\pi\)
\(558\) −105.648 366.407i −0.189333 0.656643i
\(559\) −66.8345 −0.119561
\(560\) −66.2182 3.65995i −0.118247 0.00653563i
\(561\) 2399.87i 4.27785i
\(562\) −136.416 473.116i −0.242732 0.841843i
\(563\) 533.508 220.986i 0.947616 0.392515i 0.145282 0.989390i \(-0.453591\pi\)
0.802334 + 0.596875i \(0.203591\pi\)
\(564\) −458.213 + 646.397i −0.812434 + 1.14609i
\(565\) 89.9132 + 37.2433i 0.159138 + 0.0659173i
\(566\) −254.517 319.009i −0.449676 0.563620i
\(567\) 10.5438 + 10.5438i 0.0185958 + 0.0185958i
\(568\) 11.5225 + 10.2833i 0.0202860 + 0.0181045i
\(569\) −663.220 663.220i −1.16559 1.16559i −0.983232 0.182356i \(-0.941628\pi\)
−0.182356 0.983232i \(-0.558372\pi\)
\(570\) −464.643 52.2486i −0.815164 0.0916642i
\(571\) 602.590 + 249.601i 1.05532 + 0.437130i 0.841789 0.539806i \(-0.181502\pi\)
0.213535 + 0.976935i \(0.431502\pi\)
\(572\) −119.372 189.793i −0.208692 0.331805i
\(573\) 5.08344 2.10563i 0.00887162 0.00367474i
\(574\) 59.5426 107.791i 0.103733 0.187788i
\(575\) 605.918i 1.05377i
\(576\) 591.122 743.266i 1.02625 1.29039i
\(577\) −920.164 −1.59474 −0.797369 0.603492i \(-0.793775\pi\)
−0.797369 + 0.603492i \(0.793775\pi\)
\(578\) 419.981 + 231.994i 0.726610 + 0.401374i
\(579\) −377.462 911.274i −0.651920 1.57388i
\(580\) 132.702 83.4639i 0.228796 0.143903i
\(581\) 18.1455 43.8071i 0.0312315 0.0753994i
\(582\) −100.512 + 893.848i −0.172701 + 1.53582i
\(583\) 1300.80 1300.80i 2.23122 2.23122i
\(584\) 258.406 + 230.618i 0.442477 + 0.394894i
\(585\) −43.1105 + 43.1105i −0.0736932 + 0.0736932i
\(586\) −148.308 + 118.325i −0.253085 + 0.201920i
\(587\) 377.814 912.123i 0.643635 1.55387i −0.178106 0.984011i \(-0.556997\pi\)
0.821741 0.569861i \(-0.193003\pi\)
\(588\) −111.530 79.0604i −0.189676 0.134456i
\(589\) 150.290 + 362.833i 0.255162 + 0.616014i
\(590\) −201.469 + 58.0905i −0.341473 + 0.0984584i
\(591\) −603.071 −1.02042
\(592\) −476.108 531.818i −0.804237 0.898341i
\(593\) 544.070i 0.917488i 0.888568 + 0.458744i \(0.151701\pi\)
−0.888568 + 0.458744i \(0.848299\pi\)
\(594\) 1170.84 337.593i 1.97111 0.568338i
\(595\) 88.0686 36.4792i 0.148014 0.0613096i
\(596\) 55.3757 + 325.047i 0.0929123 + 0.545381i
\(597\) 138.783 + 57.4857i 0.232467 + 0.0962909i
\(598\) 110.193 87.9158i 0.184269 0.147016i
\(599\) −734.945 734.945i −1.22695 1.22695i −0.965111 0.261843i \(-0.915670\pi\)
−0.261843 0.965111i \(-0.584330\pi\)
\(600\) −831.403 290.301i −1.38567 0.483835i
\(601\) 234.797 + 234.797i 0.390677 + 0.390677i 0.874929 0.484252i \(-0.160908\pi\)
−0.484252 + 0.874929i \(0.660908\pi\)
\(602\) −15.0685 + 134.003i −0.0250308 + 0.222597i
\(603\) 263.531 + 109.158i 0.437034 + 0.181025i
\(604\) 91.0504 399.733i 0.150746 0.661810i
\(605\) −486.030 + 201.320i −0.803356 + 0.332761i
\(606\) −852.921 471.146i −1.40746 0.777469i
\(607\) 171.314i 0.282231i −0.989993 0.141116i \(-0.954931\pi\)
0.989993 0.141116i \(-0.0450689\pi\)
\(608\) −519.434 + 828.707i −0.854331 + 1.36301i
\(609\) 323.157 0.530636
\(610\) 139.836 253.146i 0.229239 0.414994i
\(611\) −40.7176 98.3010i −0.0666409 0.160885i
\(612\) −303.156 + 1330.93i −0.495353 + 2.17472i
\(613\) −325.003 + 784.627i −0.530185 + 1.27998i 0.401216 + 0.915984i \(0.368588\pi\)
−0.931401 + 0.363996i \(0.881412\pi\)
\(614\) −755.696 84.9772i −1.23078 0.138399i
\(615\) −125.871 + 125.871i −0.204668 + 0.204668i
\(616\) −407.448 + 196.550i −0.661441 + 0.319074i
\(617\) 51.8933 51.8933i 0.0841059 0.0841059i −0.663802 0.747908i \(-0.731058\pi\)
0.747908 + 0.663802i \(0.231058\pi\)
\(618\) −1178.48 1477.10i −1.90693 2.39013i
\(619\) −182.924 + 441.618i −0.295516 + 0.713438i 0.704477 + 0.709726i \(0.251181\pi\)
−0.999993 + 0.00371167i \(0.998819\pi\)
\(620\) −13.5230 79.3782i −0.0218113 0.128029i
\(621\) 293.182 + 707.803i 0.472112 + 1.13978i
\(622\) 11.7146 + 40.6284i 0.0188337 + 0.0653190i
\(623\) −132.767 −0.213109
\(624\) 67.8381 + 193.321i 0.108715 + 0.309810i
\(625\) 446.946i 0.715113i
\(626\) −34.5841 119.944i −0.0552461 0.191604i
\(627\) −2946.63 + 1220.53i −4.69956 + 1.94662i
\(628\) −305.199 216.347i −0.485985 0.344502i
\(629\) 947.889 + 392.628i 1.50698 + 0.624211i
\(630\) 76.7169 + 96.1563i 0.121773 + 0.152629i
\(631\) 808.102 + 808.102i 1.28067 + 1.28067i 0.940287 + 0.340382i \(0.110556\pi\)
0.340382 + 0.940287i \(0.389444\pi\)
\(632\) 23.3930 + 411.671i 0.0370143 + 0.651378i
\(633\) 264.952 + 264.952i 0.418565 + 0.418565i
\(634\) 862.669 + 97.0062i 1.36068 + 0.153007i
\(635\) −251.334 104.106i −0.395802 0.163946i
\(636\) −1422.94 + 894.969i −2.23732 + 1.40718i
\(637\) 16.9609 7.02544i 0.0266263 0.0110290i
\(638\) 517.054 936.028i 0.810430 1.46713i
\(639\) 28.6457i 0.0448289i
\(640\) 141.577 142.016i 0.221214 0.221900i
\(641\) 672.727 1.04950 0.524748 0.851257i \(-0.324159\pi\)
0.524748 + 0.851257i \(0.324159\pi\)
\(642\) 383.623 + 211.910i 0.597543 + 0.330078i
\(643\) −249.894 603.297i −0.388637 0.938253i −0.990229 0.139449i \(-0.955467\pi\)
0.601592 0.798803i \(-0.294533\pi\)
\(644\) −151.427 240.758i −0.235135 0.373848i
\(645\) 74.5959 180.090i 0.115653 0.279210i
\(646\) 157.091 1397.00i 0.243174 2.16253i
\(647\) −368.671 + 368.671i −0.569816 + 0.569816i −0.932077 0.362261i \(-0.882005\pi\)
0.362261 + 0.932077i \(0.382005\pi\)
\(648\) −45.0147 + 2.55794i −0.0694671 + 0.00394744i
\(649\) −1011.34 + 1011.34i −1.55830 + 1.55830i
\(650\) 92.4411 73.7527i 0.142217 0.113466i
\(651\) 63.5202 153.351i 0.0975733 0.235563i
\(652\) 80.6126 113.719i 0.123639 0.174416i
\(653\) 416.567 + 1005.68i 0.637928 + 1.54010i 0.829435 + 0.558604i \(0.188663\pi\)
−0.191506 + 0.981491i \(0.561337\pi\)
\(654\) −1357.76 + 391.489i −2.07608 + 0.598607i
\(655\) −0.163127 −0.000249049
\(656\) 123.290 + 351.345i 0.187942 + 0.535586i
\(657\) 642.418i 0.977804i
\(658\) −206.274 + 59.4758i −0.313486 + 0.0903888i
\(659\) 1085.75 449.733i 1.64758 0.682448i 0.650546 0.759467i \(-0.274540\pi\)
0.997030 + 0.0770186i \(0.0245401\pi\)
\(660\) 644.644 109.823i 0.976733 0.166398i
\(661\) 821.859 + 340.425i 1.24336 + 0.515015i 0.904762 0.425917i \(-0.140049\pi\)
0.338594 + 0.940932i \(0.390049\pi\)
\(662\) −194.093 + 154.854i −0.293192 + 0.233919i
\(663\) −208.232 208.232i −0.314075 0.314075i
\(664\) 62.2933 + 129.134i 0.0938152 + 0.194479i
\(665\) −89.5802 89.5802i −0.134707 0.134707i
\(666\) −147.946 + 1315.68i −0.222142 + 1.97549i
\(667\) 621.143 + 257.286i 0.931249 + 0.385736i
\(668\) 123.109 + 28.0414i 0.184294 + 0.0419782i
\(669\) 1237.20 512.464i 1.84932 0.766015i
\(670\) 52.7227 + 29.1236i 0.0786906 + 0.0434680i
\(671\) 1972.70i 2.93994i
\(672\) 402.904 92.4292i 0.599560 0.137544i
\(673\) −2.21034 −0.00328430 −0.00164215 0.999999i \(-0.500523\pi\)
−0.00164215 + 0.999999i \(0.500523\pi\)
\(674\) −117.803 + 213.259i −0.174782 + 0.316409i
\(675\) 245.951 + 593.777i 0.364371 + 0.879670i
\(676\) 632.292 + 144.022i 0.935344 + 0.213051i
\(677\) 21.0269 50.7634i 0.0310589 0.0749829i −0.907589 0.419860i \(-0.862079\pi\)
0.938648 + 0.344877i \(0.112079\pi\)
\(678\) −602.808 67.7851i −0.889098 0.0999781i
\(679\) −172.328 + 172.328i −0.253797 + 0.253797i
\(680\) −95.0174 + 272.123i −0.139731 + 0.400181i
\(681\) −801.975 + 801.975i −1.17764 + 1.17764i
\(682\) −342.551 429.350i −0.502274 0.629546i
\(683\) −390.373 + 942.445i −0.571557 + 1.37986i 0.328672 + 0.944444i \(0.393399\pi\)
−0.900229 + 0.435417i \(0.856601\pi\)
\(684\) 1788.33 304.663i 2.61451 0.445414i
\(685\) 82.1871 + 198.417i 0.119981 + 0.289660i
\(686\) −10.2620 35.5906i −0.0149592 0.0518814i
\(687\) −342.435 −0.498449
\(688\) −271.966 303.789i −0.395299 0.441553i
\(689\) 225.736i 0.327628i
\(690\) 113.906 + 395.048i 0.165081 + 0.572534i
\(691\) 814.515 337.383i 1.17875 0.488253i 0.294673 0.955598i \(-0.404789\pi\)
0.884075 + 0.467345i \(0.154789\pi\)
\(692\) 367.275 518.112i 0.530745 0.748716i
\(693\) 775.208 + 321.102i 1.11863 + 0.463350i
\(694\) −775.787 972.364i −1.11785 1.40110i
\(695\) 81.1516 + 81.1516i 0.116765 + 0.116765i
\(696\) −650.627 + 729.026i −0.934810 + 1.04745i
\(697\) −378.443 378.443i −0.542960 0.542960i
\(698\) 1104.35 + 124.183i 1.58216 + 0.177912i
\(699\) −152.340 63.1014i −0.217940 0.0902738i
\(700\) −127.032 201.973i −0.181475 0.288532i
\(701\) 658.869 272.913i 0.939899 0.389319i 0.140474 0.990084i \(-0.455137\pi\)
0.799425 + 0.600766i \(0.205137\pi\)
\(702\) 72.2988 130.883i 0.102990 0.186443i
\(703\) 1363.53i 1.93958i
\(704\) 376.927 1314.90i 0.535408 1.86776i
\(705\) 310.325 0.440177
\(706\) 514.731 + 284.333i 0.729081 + 0.402738i
\(707\) −101.031 243.911i −0.142901 0.344994i
\(708\) 1106.29 695.814i 1.56256 0.982787i
\(709\) −179.746 + 433.945i −0.253520 + 0.612052i −0.998483 0.0550534i \(-0.982467\pi\)
0.744963 + 0.667106i \(0.232467\pi\)
\(710\) 0.675918 6.01089i 0.000951997 0.00846604i
\(711\) 540.800 540.800i 0.760619 0.760619i
\(712\) 267.305 299.515i 0.375429 0.420667i
\(713\) 244.185 244.185i 0.342476 0.342476i
\(714\) −464.453 + 370.557i −0.650494 + 0.518987i
\(715\) −33.6053 + 81.1304i −0.0470005 + 0.113469i
\(716\) −189.102 134.049i −0.264109 0.187220i
\(717\) 676.775 + 1633.88i 0.943898 + 2.27877i
\(718\) −557.099 + 160.631i −0.775904 + 0.223720i
\(719\) 359.024 0.499338 0.249669 0.968331i \(-0.419678\pi\)
0.249669 + 0.968331i \(0.419678\pi\)
\(720\) −371.381 20.5266i −0.515807 0.0285092i
\(721\) 511.979i 0.710096i
\(722\) −1101.42 + 317.579i −1.52552 + 0.439860i
\(723\) 760.222 314.894i 1.05148 0.435538i
\(724\) −72.2004 423.805i −0.0997243 0.585366i
\(725\) 521.078 + 215.837i 0.718728 + 0.297707i
\(726\) 2563.21 2045.02i 3.53059 2.81683i
\(727\) −115.686 115.686i −0.159128 0.159128i 0.623052 0.782180i \(-0.285892\pi\)
−0.782180 + 0.623052i \(0.785892\pi\)
\(728\) −18.2992 + 52.4076i −0.0251362 + 0.0719884i
\(729\) −826.621 826.621i −1.13391 1.13391i
\(730\) 15.1584 134.802i 0.0207649 0.184661i
\(731\) 541.460 + 224.280i 0.740711 + 0.306813i
\(732\) −400.338 + 1757.58i −0.546910 + 2.40107i
\(733\) −716.650 + 296.846i −0.977694 + 0.404974i −0.813571 0.581466i \(-0.802479\pi\)
−0.164123 + 0.986440i \(0.552479\pi\)
\(734\) −668.146 369.079i −0.910281 0.502832i
\(735\) 53.5437i 0.0728486i
\(736\) 848.013 + 143.118i 1.15219 + 0.194454i
\(737\) 410.854 0.557468
\(738\) 333.942 604.538i 0.452496 0.819157i
\(739\) 53.5571 + 129.298i 0.0724724 + 0.174964i 0.955965 0.293482i \(-0.0948141\pi\)
−0.883492 + 0.468446i \(0.844814\pi\)
\(740\) −62.0890 + 272.586i −0.0839040 + 0.368359i
\(741\) −149.770 + 361.576i −0.202118 + 0.487956i
\(742\) −452.600 50.8944i −0.609973 0.0685908i
\(743\) −376.827 + 376.827i −0.507169 + 0.507169i −0.913657 0.406487i \(-0.866754\pi\)
0.406487 + 0.913657i \(0.366754\pi\)
\(744\) 218.064 + 452.048i 0.293097 + 0.607591i
\(745\) 91.3176 91.3176i 0.122574 0.122574i
\(746\) −839.857 1052.67i −1.12581 1.41108i
\(747\) 101.768 245.690i 0.136236 0.328902i
\(748\) 330.193 + 1938.19i 0.441435 + 2.59116i
\(749\) 45.4413 + 109.705i 0.0606693 + 0.146469i
\(750\) 201.514 + 698.891i 0.268686 + 0.931855i
\(751\) −373.722 −0.497633 −0.248816 0.968551i \(-0.580042\pi\)
−0.248816 + 0.968551i \(0.580042\pi\)
\(752\) 281.126 585.088i 0.373838 0.778042i
\(753\) 2051.35i 2.72424i
\(754\) −36.3535 126.081i −0.0482142 0.167216i
\(755\) −148.347 + 61.4474i −0.196486 + 0.0813873i
\(756\) −246.120 174.468i −0.325556 0.230778i
\(757\) −39.6819 16.4368i −0.0524200 0.0217131i 0.356319 0.934364i \(-0.384032\pi\)
−0.408739 + 0.912651i \(0.634032\pi\)